This Helical Spring Design spreadsheet from 3D-LABS follows ISO standards and gives instant, checkable results for practising engineers — no manual derivation required.
This spreadsheet designs close-coiled helical compression and extension springs per DIN 2098-1:1983, ISO 10243:2010, and the Spring Design Manual (SAE, 2nd Ed.) using the Wahl correction factor for stress and the Bergsträsser approximation — the two standard methods for shear stress in spring wire under combined torsion and direct shear.
What standard does this calculation follow?
DIN 2098-1:1983 (compression springs), ISO 10243:2010 (extension springs), SAE Spring Design Manual 2nd Edition, DIN EN 13906-1:2013 (helical springs — cylindrical compression springs). Material: DIN 17223-1 (patented cold-drawn wire), EN 10270-1 (unalloyed spring steel wire), ASTM A227/A228.
What formula is used?
Wahl correction factor: Kw = (4C-1)/(4C-4) + 0.615/C, where C = D/d (spring index). Bergsträsser factor: KB = (4C+2)/(4C-3). Shear stress: τ = Kw × 8FD/(πd³). Spring rate: k = Gd⁴/(8D³na), where G = shear modulus (79,000 MPa for steel), na = active coils.
Frequently Asked Questions
What is the Wahl correction factor for a helical spring?
Wahl correction factor Kw = (4C-1)/(4C-4) + 0.615/C, where C = D/d (spring index = mean coil diameter / wire diameter). For C = 6: Kw = 23/20 + 0.1025 = 1.253. It corrects shear stress for curvature and direct shear. For spring index C 12, coils become difficult to manufacture.
What is the difference between Wahl and Bergsträsser correction factors?
Bergsträsser: KB = (4C+2)/(4C-3). Wahl: Kw = (4C-1)/(4C-4) + 0.615/C. For C = 6: KB = 1.253, Kw = 1.253 — nearly identical. Bergsträsser is simpler and preferred for calculations. Both give identical results to within ±1% for C ≥ 4, which covers 95% of practical spring designs.
What inputs does this spring design spreadsheet require?
Required inputs: applied force F (N), spring outer diameter OD (mm) or wire diameter d (mm), free length Lf (mm), number of active coils na, material (spring steel G = 79,000 MPa or stainless G = 69,000 MPa), and end condition (closed-ground, closed-unground, open). Output: spring rate k (N/mm), shear stress τ (MPa), factor of safety against yielding, solid height, and buckling check per DIN 2098.
What’s Included
An instant Excel download with the complete formula set, a worked numerical example, and reference to the governing standard — ready to adapt to your own project inputs.
